Apparatuses and methods for mapping image coordinates to ground coordinates

Abstract

A method for photogrammetric block adjustment of satellite imagery using a simplified adjustment model in-lieu of a physical camera model. A known relationship between image space line and sample coordinate and object space X, Y, Z coordinates is provided by a mathematical model. Observations comprise ground control points, tie points, or other observations for which approximate knowledge of object and image space coordinates is available. The photogrammetric block adjustment determines the parameters of the adjustment model to best fit the observations and measurements. Object coordinates can be calculated for features measured in the images after block adjustment. In one embodiment the method is utilized for photogrammetric block adjustment of satellite imagery described by a rational polynomial (RPC) camera model rather than by a physical camera model.

We claim:  
     
       1. A method performed on a processor of adjusting at least one image to provide a relationship between a ground coordinate space and an image coordinate space, the method comprising the steps of: 
       obtaining an image having an image coordinate space;  
       establishing a nominal relationship between the image coordinate space and a ground coordinate space;  
       fitting a nominal parametric equation having at least one coefficient to the established nominal relationship such that the nominal parametric equation describes the established nominal relationship between the image coordinate space and the ground coordinate space;  
       developing an adjustment model by combining the fitted nominal equation with a parametric adjustment equation having at least one adjustable coefficient;  
       measuring GCP ground coordinates and the GCP image coordinates of at least one ground control point (GCP);  
       forming observation equations using the measured GCP ground coordinates and GCP image coordinates; and  
       solving for the at least one adjustable coefficient of the developed adjustment model using the formed observation equations and the developed adjustment model.  
     
     
       2. The method of  claim 1 , further comprising the steps of: 
       obtaining at least one other image, the image and the at least one other image having at least one overlapping portion such that at least one tie point (TP) exists in the at least one overlapping portion; and  
       measuring the TP image coordinates of the at least one tie point in the overlapping portion,  
       wherein the forming observation equations uses the measured TP image coordinates.  
     
     
       3. The method of  claim 1 , wherein the obtaining step includes automatically obtaining any images. 
     
     
       4. The method of  claim 1 , wherein the establishing the nominal relationship step uses a physical camera model. 
     
     
       5. The method of  claim 4 , wherein the establishing the nominal relationship step includes using exterior and interior orientation parameters of an imaging device. 
     
     
       6. The method of  claim 1 , wherein the fitting the nominal parametric equation step uses a rational polynomial. 
     
     
       7. The method of  claim 1 , wherein the fitting the nominal parametric equation step uses a polynomial. 
     
     
       8. The method of  claim 1 , wherein the fitting the nominal parametric equation step uses an orthogonal polynomial. 
     
     
       9. The method of  claim 1 , wherein a range of the adjustment model is in the image coordinate space. 
     
     
       10. The method of  claim 1 , wherein a range of the adjustment model is in the ground coordinate space. 
     
     
       11. The method of  claim 1 , wherein a domain of the adjustment model is in the image coordinate space. 
     
     
       12. The method of  claim 1 , wherein a domain of the adjustment model is in the ground coordinate space. 
     
     
       13. The method of  claim 1 , wherein the adjustment model is an offset. 
     
     
       14. The method of  claim 1 , wherein the adjustment model is an affine transformation. 
     
     
       15. The method of  claim 1 , wherein the adjustment model is a polynomial model. 
     
     
       16. The method of  claim 1 , wherein the adjustment model is a Fourier series. 
     
     
       17. The method of  claim 1 , wherein the adjustment model is a wavelet model. 
     
     
       18. The method of  claim 1 , wherein the solving step includes using least squares. 
     
     
       19. The method of  claim 1 , wherein the solving step includes using a robust estimation. 
     
     
       20. The method of  claim 18 , wherein the least squares is a non-linear least squares. 
     
     
       21. The method of  claim 1 , wherein the solving step is iterated until convergence is achieved. 
     
     
       22. A method performed on a processor of adjusting a plurality of images to provide a relationship between a ground coordinate space and an image coordinate space, the method comprising the steps of: 
       obtaining a plurality of images, each image having an image coordinate space, wherein the images form at least one overlapping portion such that at least one tie point (TP) exists in the at least one overlapping portion;  
       establishing a nominal relationship between the image coordinate space and a ground coordinate space;  
       fitting a nominal parametric equation having at least one coefficient to the established nominal relationship such that the nominal parametric equation describes the established nominal relationship between the image coordinate space and the ground coordinate space;  
       developing an adjustment model by combining the fitted nominal equation with a parametric adjustment equation having at least one adjustable coefficient;  
       measuring TP image coordinates of the at least one tie point;  
       forming observation equations using the measured TP image coordinates; and  
       solving for the at least one adjustable coefficient of the developed adjustment model using the observation equations and the developed adjustment model.  
     
     
       23. The method of  claim 22 , further comprising the step of: 
       measuring GCP ground coordinates of at least one ground control point,  
       wherein the forming observation equations uses the measured GCP ground coordinates.  
     
     
       24. The method of  claim 22 , wherein the obtaining step includes automatically obtaining the plurality of images. 
     
     
       25. The method of  claim 22 , wherein the establishing the nominal relationship step uses a physical camera model. 
     
     
       26. The method of  claim 25 , wherein the establishing the nominal relationship step includes using exterior and interior orientation parameters of an imaging device. 
     
     
       27. The method of  claim 22 , wherein the fitting the nominal parametric equation step uses a rational polynomial. 
     
     
       28. The method of  claim 22 , wherein the fitting the nominal parametric equation step uses a polynomial. 
     
     
       29. The method of  claim 22 , wherein the fitting the nominal parametric equation step uses an orthogonal polynomial. 
     
     
       30. The method of  claim 22 , wherein a range of the adjustment model is in the image coordinate space. 
     
     
       31. The method of  claim 22 , wherein a range of the adjustment model is in the ground coordinate space. 
     
     
       32. The method of  claim 22 , wherein a domain of the adjustment model is in the image coordinate space. 
     
     
       33. The method of  claim 22 , wherein a domain of the adjustment model is in the ground coordinate space. 
     
     
       34. The method of  claim 22 , wherein the adjustment model is an offset. 
     
     
       35. The method of  claim 22 , wherein the adjustment model is an affine transformation. 
     
     
       36. The method of  claim 22 , wherein the adjustment model is a polynomial model. 
     
     
       37. The method of  claim 22 , wherein the adjustment model is a Fourier series. 
     
     
       38. The method of  claim 22 , wherein the adjustment model is a wavelet model. 
     
     
       39. The method of  claim 22 , wherein the solving step includes using least squares. 
     
     
       40. The method of  claim 22 , wherein the solving step includes using a robust estimation. 
     
     
       41. The method of  claim 39 , wherein the least squares is a non-linear least squares. 
     
     
       42. The method of  claim 22 , wherein the solving step is iterated until convergence is achieved. 
     
     
       43. A computer program product comprising: 
       a computer usable medium including computer readable code embodied therein for processing data to provide a relationship between an image coordinate space and a ground coordinate space, the computer usable medium comprising:  
       an image acquiring module configured to acquire at least an image having an image coordinate space;  
       a relational module configured to establish a nominal relationship between the image coordinate space and a ground coordinate space;  
       a fitting module configured to fit a nominal parametric equation having at least one coefficient to the established nominal relationship such that the nominal parametric equation describes the established nominal relationship between the image coordinate space and the ground coordinate space;  
       a development module configured to develop an adjustment model by combining the fitted nominal equation with a parametric adjustment model having at least one adjustable coefficient;  
       a receiving module configured to receive GCP ground coordinates and GCP image coordinates of at least one ground control point (GCP);  
       an observation module configured to form observation equations using the received GCP ground coordinates and GCP image coordinates; and  
       a calculating module configured to solve for the at least one adjustable coefficient of the developed adjustment model using the formed observation equations and the developed adjustment model.  
     
     
       44. The computer program product of  claim 43 , wherein 
       the acquiring module is further configured to acquire at least one other image, the image and the at least one other image having at least one overlapping portion where at least one tie point (TP) exists in the at least one overlapping portion; and  
       the receiving module is further configured to receive the TP image coordinates of the at least one tie point,  
       wherein the observation module is further configured to form observation equations using the received TP image coordinates.  
     
     
       45. The computer program product of  claim 43 , wherein acquiring module is configured to automatically acquire any images. 
     
     
       46. The computer program product of  claim 43 , wherein the relational module is configured to establish the nominal relationship using a physical camera model. 
     
     
       47. The computer program product of  claim 46 , wherein the relational module is configured to establish the nominal relationship using exterior and interior orientation parameters of an imaging device. 
     
     
       48. The computer program product of  claim 43 , wherein the fitting module is configured to fit a rational polynomial. 
     
     
       49. The computer program product of  claim 43 , wherein the fitting module is configured to fit a polynomial. 
     
     
       50. The computer program product of  claim 43 , wherein the fitting module is configured to fit an orthogonal polynomial. 
     
     
       51. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment model using a range in the image coordinate space. 
     
     
       52. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment model using a range in the ground coordinate space. 
     
     
       53. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment model using a domain in the image coordinate space. 
     
     
       54. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment model using a domain in the ground coordinate space. 
     
     
       55. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment module as an offset. 
     
     
       56. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment module as an affine transformation. 
     
     
       57. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment module as a polynomial model. 
     
     
       58. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment module as a Fourier series. 
     
     
       59. The computer program product of  claim 43 , wherein the development module is configured to develop an adjustment module as a wavelet model. 
     
     
       60. The computer program product of  claim 43 , wherein the calculating module is further configured to solve for the at least one adjustable coefficient using least squares. 
     
     
       61. The computer program product of  claim 43 , wherein the calculating module is further configured to solve for the at least one adjustable coefficient using a robust estimation. 
     
     
       62. The computer program product of  claim 60 , wherein the calculating module is further configured to solve for the at least one adjustable coefficient using non-linear least squares. 
     
     
       63. The computer program product of  claim 43 , wherein the calculating module is further configured to iterate the calculating step until convergence is achieved. 
     
     
       64. A computer program product comprising: 
       a computer usable medium including computer readable code embodied therein for processing data to provide a relationship between an image coordinate space and a ground coordinate space, the compute usable medium comprising:  
       an image acquiring module configured to acquire a plurality of images, each image having an image coordinate space, wherein the images form at least one overlapping portion such that at least one tie point (TP) exists in the at least one overlapping;  
       a relational module configured to establish a nominal relationship between the image coordinate space and a ground coordinate space;  
       a fitting module configured to fit a nominal parametric equation having at least one coefficient to the established nominal relationship such that the nominal parametric equation describes the established nominal relationship between the image coordinate space and the ground coordinate space;  
       a development module configured to develop an adjustment model by combining the fitted nominal equation with a parametric adjustment model having at least one adjustable coefficient;  
       a receiving module configured to receive TP image coordinates of the at least one tie point;  
       an observation module configured to form observation equations using the received TP image coordinates; and  
       a calculating module configured to solve for the at least one adjustable coefficient of the developed adjustment model using the formed tie point observation equations and the developed adjustment model.  
     
     
       65. The computer program product of  claim 64 , wherein 
       the receiving module is further configured to receive GCP ground coordinates of at least one ground control point; and  
       the observation module is further configured to form observation equations using the received GCP ground coordinates.  
     
     
       66. The computer program product of  claim 64 , wherein the image acquiring module is configured to automatically acquire the plurality of images. 
     
     
       67. The computer program product of  claim 64 , wherein the relational module is configured to establish the nominal relationship using a physical camera model. 
     
     
       68. The computer program product of  claim 67 , wherein the relational module is configured to establish the nominal relationship using exterior and interior orientation parameters of an imaging device. 
     
     
       69. The computer program product of  claim 64 , wherein the fitting module is configured to fit a rational polynomial. 
     
     
       70. The computer program product of  claim 64 , wherein the fitting module is configured to fit a polynomial. 
     
     
       71. The computer program product of  claim 64 , wherein the fitting module is configured to fit an orthogonal polynomial. 
     
     
       72. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment model using a range in the image coordinate space. 
     
     
       73. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment model using a range in the ground coordinate space. 
     
     
       74. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment model using a domain in the image coordinate space. 
     
     
       75. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment model using a domain in the ground coordinate space. 
     
     
       76. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment module as an offset. 
     
     
       77. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment module as an affine transformation. 
     
     
       78. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment module as a polynomial model. 
     
     
       79. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment module as a Fourier series. 
     
     
       80. The computer program product of  claim 64 , wherein the development module is configured to develop an adjustment module as a wavelet model. 
     
     
       81. The computer program product of  claim 64 , wherein the calculating module is further configured to solve for the at least one adjustable coefficient using least squares. 
     
     
       82. The computer program product of  claim 64 , wherein the calculating module is further configured to solve for the at least one adjustable coefficient using a robust estimation. 
     
     
       83. The computer program product of  claim 81 , wherein the calculating module is further configured to solve for the at least one adjustable coefficient using non-linear least squares. 
     
     
       84. The computer program product of  claim 64 , wherein the calculating module is further configured to iterate the calculating step until convergence is achieved.